1/4/2022

Introduction

  • Statistics exam data from 60 students
  • 30 male
  • 30 female
  • confidence level
  • fear of statistics
  • depression level
  • age
Min First Quartile Median Mean Third Quartile Max
Exam score 46 59.75 65.50 67.80 74.25 95
Confidence level 9 14.75 17.81 17.81 20.25 32
Fear of statistics 29 38.00 42.15 42.15 46.00 58

Introduction

Introduction

There seems to be an association between confidence level and exam scores, and fear of statistics and exam scores (Onwuegbuzie and Wilson 2003).

Introduction

Introduction

Regression Model

The following regression model was used: \[ exam\ scores_i = \beta_0 + \beta_1*confidence \ level_i \\+ \beta_2* fear\ of \ statistics_i + residual_i \]

Or in R code:

OLS <- lm(dat$exam ~ dat$confidc + dat$fostc, data = dat)

Convergence of the Metropolis-Hastings Algorithm

Estimates and Intervals

Mean SD Q025 Median Q975
Intercept 67.799 1.127 65.571 67.804 70.000
Confidence 1.199 0.226 0.742 1.201 1.635
Fear of statistics -0.077 0.202 -0.473 -0.078 0.320
sigma2 76.124 14.779 52.603 74.355 110.092

Testing Normality of the Outcome Variable Using a Posterior Predictive Check

When using a pppv, a replicated dataset is created. This is the dataset that would be expected if the null model is true, so if the residuals are normally distributed. The pppv tests whether the replicated data have a more extreme test statistic than the original data.

Testing Normality of the Outcome Variable Using a Posterior Predictive Check

References

Onwuegbuzie, Anthony J, and Vicki A Wilson. 2003. “Statistics Anxiety: Nature, Etiology, Antecedents, Effects, and Treatments–a Comprehensive Review of the Literature.” Teaching in Higher Education 8 (2): 195–209.